Resonant frequency of a LCR series circuit is 16 kHz. If the capacitance is increased to 16 times, then the new resonant frequency will become
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 4\,\mathrm{kHz} \)
The resonant frequency of a series LCR circuit is \( f_0 = 1/(2\pi\sqrt{LC}) \) and does not depend on \( R \). For a fixed \( L \), \( f_0 \propto 1/\sqrt{C} \).
\( \displaystyle \frac{f'}{f_0} = \sqrt{\frac{C}{C'}} = \sqrt{\frac{1}{16}} = \frac{1}{4} \)
\( \displaystyle f' = \frac{16\,\mathrm{kHz}}{4} = 4\,\mathrm{kHz} \)